In the above image, I have four symmetrical corners of an ellipse which I'm trying to join together into one ellipse that is perfectly symmetrical. I am trying to line up the anchors perfectly (one corner at time) and then do a join, yet the result is always slightly off. I've been selecting the two points I want to join and using Path -> Average, then Path -> Join to do this, yet as mentioned it's not coming out precise. Does anyone know a better way to do this?

Thanks Monika. Where is the "align to anchor point" setting? I have the selection tool selected, and in the align panel I see "Align to Selection" and "Align to Artboard" but no "Align to Anchor Point".

I believe I do have smart guides checked and I also have "snap to point" checked, yet it isn't "snapping".

Yes they are identical. I suppose I could manually just move an anchor on top of another by subtracting the distance it needs to land on the other one. Do you know how to see the exact anchor points, not the rounded ones?

I actually ended up using the 3 by 3 matrice on the transform palette (the one where you can click on the square and it gives you the exact values for the particular point) and I lined it up manually. Still am curious on how to get the exact coordinates of certain anchor points in the transform palette. I know when you click on them it gives you a rounded value, but for future reference just curious how to get the exact value. Thanks for the help.

0) If needed, under Align Objects select the two top quarters and Align>Vertical Align Top and select the two bottom quarters and Align>Vertical Align Bottom,

Then under Distribute Spacing and with the Direct Selection Tool:

1) Select the two top quarters, click the leftmost once more and Horizontal Distribute Space (with the default setting Auto), then select the coinciding end Anchor Points and Ctrl/Cmd+J (Smooth),

2) Repeat (similarly) for the bottom pair,

3) Select both halves, click the topmost once more and Vertical Distribute Space (with the default setting Auto), then select one set of coinciding end Anchor Points and Ctrl/Cmd+J (Smooth), then join the other set.